WIAS Preprint No. 422, (1998)

On Quasi-interpolation with non-uniformly distributed centers on Domains and Manifolds


  • Maz´ya, Vladimir
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 41A30 41A63 41A25


  • Approximate approximations, multivariate quasi-interpolation, nonregular centers, manifolds




The paper studies quasi-interpolation by scaled shifts of a smooth and rapidly decaying function. The centers are images of a smooth mapping of the hZn-lattice in Rs, s ≥ n, and the scaling parameters are proportional to h. We show that for a large class of generating functions the quasi-interpolants provide high order approximations up to some prescribed accuracy. Although the approximants do not converge as h tends to zero, this is not feasible in computations if a scalar parameter is suitably chosen. The lack of convergence is compensated for by more flexibility in the choice of generating functions used in numerical methods for solving operator equations.

Appeared in

  • J. Approx. Th. 10 (2001), pp. 125-145

Download Documents